Second-Order/Pseudo-Second-Order ReactionGary L. Bertrand Professor Emeritus of Chemistry Missouri University of Science and Technology (formerly University of Missouri-Rolla) background close A Second-Order Reaction is described mathematically as: _{t} = 1/[A]_{t=0} + ν_{A}ktFor a Pseudo-Second-Order Reaction, the reaction rate constant k is replaced by the apparent reaction rate constant k'. If the reaction is not written out specifically to show a value of ν_{A}, the value is assumed to be 1 and is not shown in these equations.The simplest way to confirm that these are the proper equations to describe the reaction and to get an approximate value for k or k', is with the method of half-lives. The half-life t is defined as the time required for the initial concentration to be halved:_{1/2}_{t1/2} = [A]_{t=0}/2 ._{t=0} - 1/[A]_{t=0} = 1/[A]_{t=0} = ν_{A}kt_{1/2}The time required for the concentration to be reduced to 1/4 of the initial concentration ( t) is _{3/4}_{t=0} - 1/[A]_{t=0} = 3/[A]_{t=0} = ν_{A}kt_{3/4}NOTE:The "Second-Order Kinetics" exercise is designed so that you can get an accurate value of the half-life. Scan the concentration column for a value slightly larger than half of the initial concentration. Adjust the value of "Start Time" and the value of "Interval" to get a better estimate of the half-life. The same procedure may be used to find the time for the second half-life. A better procedure is to generate data for a much different initial concentration (perhaps a ten-fold change) and confirm that the product of the half-life times the initial concentration is constant and equal to 1/k.The best values of the reaction rate constant ( k) can be obtained with data taken in the middle third of the reaction (from [A] to _{t} = (2/3)[A]_{t=0}[A]). Linear Least Squares regression with _{t} = (1/3)[A]_{t=0}Y = 1/[A] and _{t}X = t gives k or k' as the slope. |